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On the solution of the dynamic population balance model describing emulsification: Evaluation of weighted residual methods
Author(s) -
Solsvik Jannike,
Becker Per J.,
SheibatOthman Nida,
Jakobsen Hugo A.
Publication year - 2014
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.21875
Subject(s) - residual , population , galerkin method , mathematics , method of mean weighted residuals , spectral method , spectral space , collocation (remote sensing) , orthogonal collocation , transient (computer programming) , population balance equation , mathematical optimization , algorithm , computer science , collocation method , finite element method , mathematical analysis , physics , ordinary differential equation , demography , sociology , machine learning , thermodynamics , differential equation , operating system , pure mathematics
Numerical techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau and least‐squares, are evaluated for the solution of transient population balance (PB) models describing liquid–liquid emulsification systems in stirred batch vessels. The numerical solution techniques are compared based on (i) a breakage dominated system with experimental data available, and (ii) a breakage–coalescence test case. Two numerical approaches are studied for the transient term: (i) time‐differencing by a low order finite difference approximation, and (ii) the spectral‐element technique. Both approaches use spectral approximations in the phase space dimension. Based on a residual measure, computational costs, and implementation complexity the combined finite difference–spectral approach is recommended above the spectral‐in‐time‐spectral‐in‐space approach. Within this recommended solution framework, it is not necessary to use a more mathematical complex spectral method than the orthogonal collocation technique.